Abstract
In this paper, we use variational tools in order to study the existence and the multiplicity of solutions for a nonlinear elliptic problem involving fractional operators. Precisely, we use the Mountain pass theorem to prove the existence of a nontrivial solution. Also, by combining this with the Ekeland variational principle the existence of multiple solutions is proved. Moreover, the existence of infinitely many solutions is given by using the \(\mathbb {Z}2\)-symmetric version for even functionals of the Mountain pass Theorem. To illustrate the usefulness of the main results an illustrative example is presented.
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Chammem, R., Ghanmi, A. & Mechergui, M. Combined effects in nonlinear elliptic equations involving fractional operators. J. Pseudo-Differ. Oper. Appl. 14, 35 (2023). https://doi.org/10.1007/s11868-023-00530-w
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DOI: https://doi.org/10.1007/s11868-023-00530-w